Variational iteration method: New development and applications

Variational Iteration Method for Burger’s Equation in Different Positions

“…The method of VIM, that was suggested initially by [1][2][3][4], was evinced by several authors to exist as a potent tool for mathematics when it comes for problems like linear and nonlinear ones [5][6][7][8][9][10][11][12][13][14][15]. In contrast to the old-style numerical methods, the features of discretization, linearization, transformation or perturbation is no longer in need for VIM.…”

A comparison of Semi-analytical Methods for Solving Partial Integro-Differential Equations

“…He [1,2] developed the variational iteration and homotopy perturbation methods for solving linear, nonlinear partial integro-differential equation. It is worth mentioning that the origin of variational iteration method can be traced to Inokuti, Sekine and Mura [3], but the real potential of this technique was explored by He [4][5][6][7][8][9][10]. Moreover, He realized the physical significance of the variational iteration method, its compatibility with the physical problems and applied this promising technique to a wide class of linear and nonlinear, ordinary, partial integro-differential equation [1,2].…”

The Combined Laplace-homotopy Analysis Method for Partial Differential Equations

“…In recent years many authors have paid attention to studying the solutions of linear and nonlinear partial differential equations by using various methods. Among these are the Adomian decomposition method (ADM) [8], Hes semi-inverse method [9], the tanh method, the homotopy perturbation method (HPM), the sinhcosh method, the differential transform method and the variational iteration method (VIM) [10,11,12,13,14,15,16,17,18,19]. Most of these methods have their inbuilt deficiencies like the calculation of Adomians polynomials, the Lagrange multiplier, divergent results and huge computational work.…”